Basis pursuit

Basis pursuit is a technique in signal processing and data analysis that aims to find the simplest possible explanation of complex data by expressing it as a combination of a few basic building blocks, called basis functions. It focuses on identifying the sparsest combination—using the fewest components—while still accurately representing the original data. This approach is especially useful in scenarios like compressed sensing or image reconstruction, where recovering original signals from limited or noisy measurements requires finding the most straightforward, efficient representation.